A rhombus.
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Yes it is - by definition, a parallelogram is described as having opposite sides and angles equal. A square is a 'special' type of parallelogram.
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A parallelogram can be a square, but never can a square be a parallelogram. A square is defined as having all four sides the same and all four right angles. A parallelogram has to have two pairs of parallel sides.
Some shapes having four equal sides include rhombus, square, diamond, parallelogram with four equal sides, and oblique-angled equilateral parallelogram.
A rectangle cannot be a parallelogram because a parallelogram has opposite sides that are parallel and equal in length, while a rectangle has all angles equal to 90 degrees. Thus, a rectangle is a specific type of parallelogram that has the additional property of having all angles equal to 90 degrees.